On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta

0556312 - MÚ 2023 RIV DE eng J - Journal Article
Fröb, M. B. - Khavkine, Igor - Málek, Tomáš - Pravda, Vojtěch
On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta.
European Physical Journal C. Roč. 82, č. 3 (2022), č. článku 215. ISSN 1434-6044. E-ISSN 1434-6052
R&D Projects: GA ČR(CZ) GA19-09659S
Grant - others:AV ČR(CZ) AP1801
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : black hole * well-posedness * Einstein-Maxwell theory
OECD category: Pure mathematics
Impact factor: 4.4, year: 2022
Method of publishing: Open access
https://doi.org/10.1140/epjc/s10052-022-10160-z

We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein-Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type II on the horizon and type D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr-Schild form with a geodesic Kerr-Schild vector.
Permanent Link: http://hdl.handle.net/11104/0330595